Question: Carl is on the school track team. To prepare for an upcoming race, he plans to run $217$ miles total over the next $31$ days. Write an equation to determine how many miles, $m$, he needs to run per day, assuming he runs the same amount each day. How many miles does Carl need to run each day?
Explanation: Carl will run an unknown number of miles, ${m}$, per day. We know he plans to run ${217}$ miles total over ${31}$ days. To figure out how many miles Carl will run per day, we need to divide the total miles by the number of days. We can find out how many miles Carl will run per day by solving this equation: ${m}=\dfrac{{217}}{{31}}$ Other ways to represent the situation with an equation include: ${31}{{m}}={217}$ or $\dfrac{{217}}{{m} }={31}$. Now we can solve for ${m}$. Since $ m$ is already by itself, we can solve by dividing $\dfrac{{217}}{{31} }$. $\begin{aligned} m &= \dfrac{{217}}{{31} } \\ \\ {m} &={7} \end{aligned}$ The following equation matches this situation: $ m = \dfrac{{217}}{{31}}$ Carl needs to run ${7}$ miles each day.